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Arctic Sea Ice Loss Has a Larger Impact than Antarctic Sea Ice Gains

Posted on 6 October 2012 by Tamino

This is a partial re-post from tamino's Open Mind blog.  For the full post, head over to Open Mind.

In this post, I’d like to compare the albedo feedback between Arctic and Antarctic sea ice changes.

First of all, for most of the year higher latitudes receive less solar energy than lower latitudes. But deep in the heart of summer this is no longer true. In fact at the point of midsummer, the poles receive more solar energy than any other place on earth. Here’s the solar insolation as a function of latitude, for various times of year from northern midwinter (southern midsummer) to northern midsummer (southern midwinter) (note: this does not include the correction for varying earth-sun distance, it’s merely to illustrate the latitude dependence at a given time of year):

insolation

During the summer months, when ice albedo feedback really counts, higher latitudes really do get more solar energy than lower latitudes. When the insolation depends strongly on latitude, with higher latitudes getting much less solar energy, the total insolation is so small that the impact of albedo change is small.

Another factor is that earth is farthest from the sun during northern hemisphere summer (when albedo change counts most) but closest to the sun in southern hemisphere summer. That has lead some to believe that the impact of albedo change will be enhanced in the southern hemisphere. This is an understandable mistake; in southern hemisphere summer earth really does receive more solar energy per unit of time because we really are closer to the sun. But the rate of travel of the earth along its orbit is inversely proportional to the square of our distance from the sun — exactly the same proportion by which solar energy changes — so the northern hemisphere summer may be weaker than the southern, but it also lasts longer. For total insolation, the two factors cancel each other so at any given latitude, the annual-total solar energy input is unaffected (a fact which was emphasized by Peter Huybers in relation to ice age cycles). So no, proximity to the sun during southern hemisphere summer doesn’t enhance the ice albedo effect.

If we really want to know the relative impact of ice albedo change between hemispheres, the thing to do is: the math.

I took daily values of sea ice area from NSIDC. I modelled the Arctic ice pack as a circle around the pole of the same area, and the Antarctic ice pack as a ring around the Antarctic continent, with the edge of the Antarctic continent as being at latitude 70S. This is only a crude representation of the geometery of the sea ice packs, but it’s at least correct to first order.

Then I computed, for each day, the sun’s declination (its altitude above or below the celestial equator). I also computed the earth-sun distance so I could apply that correction to the solar insolation. This enabled me to compute the total amount of solar radiation hitting parts of the earth which are covered by sea ice, which I call “sea ice insolation“. I did so separately for the northern and southern hemispheres.

For both hemispheres, sea ice insolation shows a strong annual cycle. So I computed the average total sea ice insolation for each year, for each hemisphere, corrected for earth-sun distance and angle of elevation of the sun. This gives the annual average sea ice insolation in TW (teraWatts). We can then look at the trends in sea ice insolation, to see which pole has lost or gained more in terms of solar energy impacting sea-ice-covered regions.

It’s quite a complicated calculation, so it’s possible I’ve made an error. But the amounts are certainly in the right ballpark, and I’ve done orbital calculations for decades, so I suspect I got it right. The data cover the time span from 1979 through 2011 (2012 isn’t over yet so is not included).

And here’s the result: annual average sea ice insolation, together with linear trend lines, for both hemispheres:

ice insolation

Since 2012 is incomplete, this doesn’t include this year’s ever-so-slightly record high Antarctic sea ice or way-astounding record low Arctic sea ice. But you can see the trends. Clearly. The trend has shown an increase in Antarctic sea ice insolation of about 53 TW, and a decrease in Arctic sea ice insolation of about 329 TW. That’s over 6 times as great.

If we spread 53 TW over the entire earth we get a global average of 0.10 W/m^2. So even if the difference between ice and ocean albedo were equal to 1 in the southern hemisphere (i.e., Antarctic sea ice were perfectly reflective while ocean was completely absorbing) the net global climate forcing would amount to -0.10 W/m^2. But sea ice isn’t perfectly reflecting, not even in the southern hemisphere where the sea ice is often snow-covered, and ocean is not perfectly absorbing. If the top-of-atmosphere (TOA) albedo difference between sea-ice-covered and open ocean areas is 0.2, then the global climate forcing from Antarctic sea ice changes would be about -0.02 W/m^2.

If we spread 329 TW over the entire earth we get a global average of 0.65 W/m^2. If the TOA albedo difference between sea ice and open ocean is 0.2, then the global climate forcing from Arctic sea ice changes would be about +0.13 W/m^2.

And it turns out that 0.2 is not a bad figure for the TOA albedo difference, according to Hudson (2011):

TOA insolation

In fact Hudson states that

"Results show that the globally and annually averaged radiative forcing caused by the observed loss of sea ice in the Arctic between 1979 and 2007 is approximately 0.1 W m-2"

so my crude calculation is certainly in the right ballpark. As I said, this is a pretty complex calculation so I may have made an error, but I certainly ended up in the right neighborhood according to Hudson.

Note: this post has been incorporated into the Intermediate rebuttal to the myth 'Arctic sea ice loss is matched by Antarctic sea ice gain'

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Comments

Comments 1 to 5:

  1. This is a great article. I had no idea that the insolation at the poles at midsummer is higher than all other latitudes, although getting sunlight for 24hrs makes it understandable. The other bit of info that stands out for me is how massive the impact of the albedo change is: 0.1W/m2 averaged over the whole world, and its impact is focussed on the Arctic. No wonder the temperature there is rising so much faster than elsewhere.
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  2. Great article by Tamino. Even better comment thread on Tamino's site, which is a must read if you want to understand the details of insolation variances discussed.

    I have a question re counter-intuitive result of total solar energy input in NH vs SH being unaffected by orbital eccentricity (the Earth being on eliptical orbit closest to Sun in Jan). Eccentricity cycle of 100ka does match the last few glacial cycles. Based on that some poeple argue that changes in eccentricity have been dominant forcings in glacial/interglacial triggering model. But the fact that eccentricity does not affect the total insolation suggest that paradoxically, the forcings we are talking about here are very weak at best. Therefore other forcings must explain the triggering of glacials. Other orbital cycles (tilt and precession) are 41ka and 26ka respectively, so how do they coincide with 100ka glaciations? Tamino mentions Peter Huybers having the explanation, but does not provide the source. Does anyone have a pointer to this source? Thanks.
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  3. Chris, early last year Tamino looked at eccentricity vs a vis obliquity and precession in three posts,

    Glacial Cycles, part 1
    http://tamino.wordpress.com/2011/01/27/glacial-cycles-part-1/

    Glacial Cycles, part 1b
    http://tamino.wordpress.com/2011/01/28/glacial-cycles-part-1b/

    and Glacial Cycles, part 2
    http://tamino.wordpress.com/2011/01/29/glacial-cycles-part-2/
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  4. Slightly off topic but of value for the discussion. I was looking at IPCC's 1st assessment report and spotted this.

    "Most model simulations suggest that the warming north of
    50°N in the winter half of the year should be enhanced due
    to feedback effects associated with sea-ice and snow cover
    (Manabe and Stouffer, 1980, Robock, 1983, Ingram et al,
    1989) In the Southern Hemisphere, results from simulations with atmospheric GCMs coupled to ocean GCMs do not show this enhancement (Bryan et al , 1988,
    Washington and Meehl, 1989, Stoutlei et al , 1989)"

    http://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_chapter_08.pdf

    So a divergence is pretty much what was expected by mainstream science from the early 90s.
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  5. Jim @3,

    Thanks for the pointers. Those are very useful posts by Tamino. Refered therein, I found this paper which answered my question in details. Great paper to learn the details of mid-Pleistocene revolution (MPR) when cycles switched from 41ka to 100ka.

    According to this and other newer studies, eccentricity just paces rather than drives the system while precession+tilt are the drivers. The ‘eccentricity myth’ (or simplified view of the relationship between glaciations and orbital forcings) an artefact of early spectral analysis of ice-core data.
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